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Two new bidirectional search algorithms

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Abstract

This paper presents two new bidirectional heuristic search algorithms for solving the shortest path problem on graphs: consistent-heuristic bucket-based bidirectional search (CBBS) and front-to-front GPU bidirectional search (FFGBS). CBBS uses a consistent heuristic and groups nodes into buckets that organize nodes based on estimated path cost and known heuristic errors. FFGBS splits the work between the CPU and GPU, with the GPU solving a front-to-front heuristic and the CPU choosing nodes to expand. This paper also includes a new front-to-front version of the GAP heuristic for the pancake problem that is efficient to solve on a GPU. Computational experiments for CBBS are performed on the pancake problem. CBBS is faster and requires less node expansions with the GAP-1 heuristic, compared to bidirectional state of the algorithms like DIBBS and DVCBS. Computational experiments for FFGBS are performed on the pancake problem and DIMACS road network, showing that FFGBS is consistently the fastest algorithm on all but the smallest pancake stacks when using the GAP-2 heuristic and is also the fastest algorithm on the largest road networks.

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Code availability

Algorithm implementation source code and testing framework are available at: https://github.com/tinamil/dibbs/releases/tag/two_algorithms-1.0

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Acknowledgements

We would like to thank the anonymous reviewers for their comments that resulted in a significantly improved manuscript.

Funding

S. H. Jacobson’s research was supported in part by the Air Force Office of Scientific Research (FA9550-19-1-0106). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the United States Air Force, Department of Defense, or the United States Government. Other authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Department of Computer Science, University of Illinois, Urbana, USA

    John A. Pavlik & Sheldon H. Jacobson

  2. Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, USA

    Edward C. Sewell

Authors
  1. John A. Pavlik
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  2. Edward C. Sewell
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  3. Sheldon H. Jacobson
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Contributions

All authors contributed to the algorithm conception and design. Algorithm C++ implementations and testing framework was written by John A. Pavlik with contributions to the testing framework from Edward C. Sewell. The first draft of the manuscript was written by John A. Pavlik and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to John A. Pavlik.

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Pavlik, J.A., Sewell, E.C. & Jacobson, S.H. Two new bidirectional search algorithms. Comput Optim Appl 80, 377–409 (2021). https://doi.org/10.1007/s10589-021-00303-5

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